Generalized confidence interval for the scale parameter of the power-law process with incomplete failure data

System testing is very time-consuming and costly, especially for complex high-cost and high-reliability systems. For this reason, the numbers of failures needed for the developmental phase of system testing should be relatively small in general. To assess reliability growth of a repairable system, the generalized confidence interval for the scale parameter of the power-law process is studied concerning incomplete failure data. Specifically, some recorded failure times in the early developmental phase of system testing cannot be observed; this circumstance is essential to establish a warranty period or determine a maintenance phase for repairable systems. The simulation results show that the proposed generalized confidence interval is not a biased estimate even for small numbers of failures, and it provides the confidence intervals that have short average widths. Therefore, the proposed method is practically useful to save business costs and time during the developmental phase of system testing since only small numbers of failures are required, and it yields precise results. Additionally, the superiority of the proposed method is presented via a numerical study using two real examples.